1. 7-9 Tessellations Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Warm Up Identify each polygon. 1. polygon with 10 sides 2. polygon with 3 congruent sides 3. polygon with 4 congruent sides and no right angles decagon equilateral triangle Course 3 7-9 Tessellations rhombus

3. Problem of the Day If each of the capital letters of the alphabet is rotated 180° around its center, which of them will look the same? Course 3 7-9 Tessellations H, I, N, O, S, X, Z

4. Learn to create tessellations. Course 3 7-9 Tessellations

5. Vocabulary tessellation regular tessellation Insert Lesson Title Here Course 3 7-9 Tessellations

6. Course 3 7-9 Tessellations Fascinating designs can be made by repeating a figure or group of figures. These designs are often used in art and architecture. A repeating pattern of plane figures that completely covers a plane with no gaps or overlaps is a tessellation.

7. Course 3 7-9 Tessellations In a regular tessellation, a regular polygon is repeated to fill a plane. The angles at each vertex add to 360°, so exactly three regular tessellations exist.

8. Course 3 7-9 Tessellations Additional Example 1: Creating a Tessellation Create a tessellation with quadrilateral EFGH. There must be a copy of each angle of quadrilateral EFGH at every vertex.

9. Course 3 7-9 Tessellations Check It Out: Example 1 Create a tessellation with quadrilateral IJKL. There must be a copy of each angle of quadrilateral IJKL at every vertex. I J K L

10. Course 3 7-9 Tessellations Additional Example 2: Creating a Tessellation by Transforming a Polygon Use rotations to create a tessellation with the quadrilateral given below. Step 1: Find the midpoint of a side. Step 2: Make a new edge for half of the side. Step 3: Rotate the new edge around the midpoint to form the edge of the other half of the side. Step 4: Repeat with the other sides.

11. Course 3 7-9 Tessellations Additional Example 2 Continued Step 5: Use the figure to make a tessellation.

12. Course 3 7-9 Tessellations Check It Out: Example 2 Use rotations to create a tessellation with the quadrilateral given below. Step 1: Find the midpoint of a side. Step 2: Make a new edge for half of the side. Step 3: Rotate the new edge around the midpoint to form the edge of the other half of the side. Step 4: Repeat with the other sides.

13. Course 3 7-9 Tessellations Step 5: Use the figure to make a tessellation. Check It Out: Example 2 Continued

14. Lesson Quiz 1. Explain why a regular tessellation with regular octagons is impossible. Each angle measure in a regular octagon is 135° and 135° is not a factor of 360° Insert Lesson Title Here Course 3 7-9 Tessellations 2. Can a semiregular tessellation be formed using a regular 12-sided polygon and a regular hexagon? Explain. No; a regular 12-sided polygon has angles that measure 150° and a regular hexagon has angles that measure 120°. No combinations of 120° and 150° add to 360°